Algorithms Seminar

How do you smoothly and continuously transform one polygon into
another in a way that appears graceful to the eye? Polygon morphing
is a key technique of two dimensional computer animation. It is
related to applications in pattern recognition, where the amount
of work involved in the morphing one shape into another measures
the degree of similarity between them, as well as in the reconstruction
of 3-D solids from 2-D contours, where morphing is used to generate
intermediate contours.

The transition between an initial and a final polygon demands
a representation of the shape that addresses two separate tasks.
The vertex correspondence problem involves matching the relevant
features of the polygons, where typically a full one-to-one matching
of vertices must be surmised from a partial matching of anchor
points supplied by the user. The vertex path problem requires
finding the motion that each vertex of the polygon will follow
from its initial to its final position. Typically, this motion
is composed of a global affine component, which seeks an optimal
alignment of the the two polygons, and a local elastic component,
which determines the deformation of the polygon features. The
solutions proposed in the literature range from linear interpolation
of vertex positions or edge lengths and angles, to fuzzy set and
distance field methods.

The seminar will present a survey of some of these approaches,
evaluating their common goals as well as assumptions, with a view
toward directions in future research into how to make metamorphosis
visually compelling.